# Bragg's Equation

Bragg's Equation

This equation gives a simple relationship between the wavelength of X-rays and the distance between the planes in the crystal and the angle of reflection. The equation may be written as:

$n \lambda = 2d \sin \theta$

where n = order of reflection; in general it is taken as $1; \lambda$ = wavelength of X-rays, d = distance between two layers of the crystals and $\theta$ =angle of incident light.

Example 1:

Inter planar distance between two layers is $4.0 \AA$ in a crystal. Calculate the angle of reflection for first order reflection. X-rays of wavelength $1.54 \AA$ are diffracted by the crystal.

$\text{Solution: Since,}n \lambda = 2d \sin \theta \\[3mm] (1)(1.54 \AA) = (2) (4 \AA) \sin \theta \\[3mm] \text{or,} \sin \theta = \dfrac{1.54}{8} = 0.1925 \\[3mm] \text{or,} \theta = \sin ^{-1} 0.1925 \\[3mm] \text{or,} \theta = 11.1^0$

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